Practice All-pairs Shortest Paths - 1 | 1. All-pairs Shortest Paths | Design & Analysis of Algorithms - Vol 2
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Knowledge

1 - All-pairs Shortest Paths

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define the All-pairs Shortest Paths problem.

💡 Hint: What does 'all-pairs' refer to?

Question 2

Easy

What does the Floyd-Warshall algorithm compute?

💡 Hint: Recall the algorithm's purpose.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does the All-pairs Shortest Paths problem focus on?

  • Finding distances from one vertex
  • Finding distances between all pairs of vertices
  • Finding cycles

💡 Hint: Think about what 'all-pairs' signifies.

Question 2

Is it true that the Bellman-Ford algorithm is applicable for finding all pairs shortest paths?

  • True
  • False

💡 Hint: Consider how Bellman-Ford works and its extensions.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

In a directed graph defined by the following edges with their weights: (1, 2) = 10, (1, 3) = 5, (2, 3) = 2, (3, 1) = 6, apply the Floyd-Warshall algorithm step-by-step to find the distance matrix for all pairs of vertices.

💡 Hint: Start with the initial weights and iteratively consider each vertex as an intermediate step.

Question 2

Analyze the impact of introducing a negative cycle in a graph, such as adding an edge with a weight of -5 between two already connected vertices, in relation to calculating the shortest paths.

💡 Hint: Reflect on paths you've calculated before and consider how negative totals would affect them.

Challenge and get performance evaluation